Shortly after the news broke that “Hamilton” had landed 16 Tony Award nominations, the musical’s director, Thomas Kail, sent a text to choreographer Andy Blankenbuehler and others on the show’s creative team. “I just woke up. What happened?” Kail asked facetiously.

What happened, as it turned out, was one for the Broadway record books.

“Hamilton,” Lin-Manuel Miranda’s hip-hop musical about America’s founding fathers, wrote its own piece of history Tuesday morning. After selling out theaters and becoming a cultural sensation since it opened on Broadway last summer, the show has now broken the record of 15 Tony nominations previously held by “The Producers” (2001) and “Billy Elliot” (2009).

In the top category of best musical, “Hamilton” will compete, nominally, against Andrew Lloyd Webber’s “School of Rock,” the small-town charmer “Waitress,” the Appalachian bluegrass piece “Bright Star” and the race-themed meta-tale “Shuffle Along, or the Making of the Musical Sensation of 1921 and All That Followed.”

But those other shows may consider it an honor just to be nominated. “Hamilton” is considered by nearly all experts to be a shoo-in to win for best musical, and it will aim for the record of 12 Tony wins (set by “The Producers”) when theater’s biggest night kicks off June 12 on CBS from New York’s Beacon Theatre.

“Hamilton” was boosted by multiple nominations in acting categories, including lead actor (Miranda and Leslie Odom Jr., the latter a front-runner) and featured actor (Daveed Diggs, Christopher Jackson and Jonathan Groff). “Hamilton” also will compete for score, choreography and direction of a musical, among others.

The nominations continue a magic-carpet ride that began with a Miranda performance of a “Hamilton Mixtape” at the White House in 2009, continued with an august run at downtown’s Public Theater in early 2015 and then a building juggernaut after opening at the Richard Rodgers in the summer.

The record set Tuesday is an industry capper of sorts on what had become the most unlikely of phenomena: a Broadway musical, often regarded as the narrowest of cultural niches, becoming a crossover hit and a gateway to a larger discussion about history and race.

“Someone asked me today if this is all old hat,” the newly minted Tony nominee Blankenbuehler recalled from the North Carolina set of “Dirty Dancing,” where, in part thanks to the success of “Hamilton” he is choreographing the new ABC reboot. “And I said, ‘Are you kidding? I’m still like a kid in a candy store.’ We all are.”

Miranda, at 36 already one of the theater world’s most influential creators, offered his own valedictory, noting in a statement that “for ‘Hamilton’ to receive a record-breaking number of nominations is an honor so humbling it’s so far been beyond my comprehension.”